Dust ion acoustic waves propagation in an inhomogeneous dusty plasma with positive and negative dust grains

The propagation of dust ion acoustic waves (DIAWs) in a collisionless, unmagnetized inhomogeneous dusty plasma containing cold positive ions, cold positive and negative dust grains, and isothermal electrons is theoretically studied. Nonlinear DIAWs are shown to be governed by a variable coefficient Kortewege-de Vries (KdV) equation. At the critical density of ions both compressive and rarefactive modified KdV solutions co-exist. Below (above) this critical point the system supports rarefactive (compressive) solitons.